After I request the current and set the Voltage source, I get the input impedance for the patch antenna, which is approximately 150 ohms, but I still cannot get the impedance of the whole patch antenna, i.e input impedance + the patch itself

The reference impedance is the impedance of the transmission line used to connect the antenna. That is, the reflection coefficient is calculated from:

Gamma = (ZL - Z0)/(ZL + Z0), where ZL is the antenna impedance, and Z0 is the "reference impedance". That is, the reflection is a function of the transmission line that connects the antenna, not just a property of the antenna itself.

The impedance of the patch antenna is the input impedance. The patch has no "intrinsic impedance" associated with it. It varies based on where you feed it: i.e., it's input impedance.

The impedance of the path antenna is just the impedance ZL. It is independent of Z0, the transmission line. That is, if you change the transmission line that feeds the antenna to a new Z0 (Z0_2), the patch impedance does not change.

So when I want to compute the impedance of the quarter wave length microstrip, which is between 50 ohms and patch antenna impedance, The quarter wavelength microstrip impedance = sqrt(50ohms*input impedance of the patch antenna), am I correct?

In the case I have input feed into patch antenna is 150, the input impedance is equal to 150 ohms+ reference impedance, the reference impedance I set to be 150 ohms too because I noticed that whenever my reference is near to 150 ohms (the same impedance of input feed), the reflection coefficient lowest = -35 dB. Please let me know if my idea is correct
Many thanks

So, if your antenna impedance is 150 Ohms, and you set the reference impedance to 150 Ohms, then the reflection coefficient will be very small (i.e. -35 dB). So yes, if you set the characteristic impedance to the antenna impedance, you will reduce the reflection coefficient.